Billionaire investor Carl Icahn and hedge-fund honcho Phil Falcone are headed for a showdown over the fate of wireless start-up LightSquared, The Post has learned.

Falcone, who has funneled a whopping $2.9 billion into LightSquared, is desperate to salvage his shaky investment amid a battle with federal regulators over building out the wireless network. Falcone has said both publicly and privately that bankruptcy is not an option.

However, some LightSquared creditors, including Icahn, would rather put the company into bankruptcy as part of a plan that would give them equity stakes in the company and greater control over its future, sources said.

The deadline for creditors to decide is fast approaching. Icahn and other owners of LightSquared’s $1.6 billion loan due 2014 have given the company until the end of April before they decide whether to put LightSquared into default for breaching some loan covenants tied to its customer contracts.

Earlier this year, Sprint canceled its deal to be LightSquared’s main carrier. In addition, LightSquared has twice failed to make “milestone” payments it owes to UK satellite company Inmarsat, which has been coordinating its wireless spectrum with LightSquared’s in an effort to create a contiguous band of wireless spectrum.

Creditors are still weighing whether to declare the loan in default based on those breaches, with Icahn leading the charge for a debt-for-equity deal that could force out Falcone, according to a person close to the talks.

Neither Icahn nor Falcone returned a request for comment. A spokesman at LightSquared also declined to comment.

If creditors can’t come to an agreement by the end of April, they could also choose to extend LightSquared’s grace period, giving them more time to settle on a plan.

Icahn, along with investors David Tepper and Andrew Beal, bought a $300 million slice of LightSquared’s first lien loan in December as LightSquared struggled with growing opposition to the rollout of its network.

The debt has recently been trading at roughly 47 cents to 48 cents on the dollar, which is up slightly after LightSquared made a recent interest payment on the loan, thus keeping it current, sources said.

In February, the FCC announced it would pull the plug on LightSquared’s ambitious launch plans following opposition from a number of industries, including agriculture and defense, that complained LightSquared’s high-powered network would interfere with GPS devices used in planes and tractors.

Last month, LightSquared accused the FCC of breach of contract, saying the company has already spent $4 billion on the project after it was “encouraged — and, indeed, affirmatively required” to aid the agency in its mandate to expand the nation’s broadband services. It also signaled that it might sue if the FCC follows through on its threat.

The spirited warning followed the company’s hire of a pair of powerhouse lawyers, including former US Solicitor General Ted Olson.